Probabilistic safety assessment of sea dikes in giao thuy nam dinh master thesis major sustainble hydraulic structures coastal engineering and management code 62 58 02 0

REASSURANCES SOCIALIST REPUBLIC OF VIETNAM INDEPENDENCE - FREEDOM - HAPPINESS REASSURANCES Dear: The management board of Thuy Loi University; The management board of Liege University

Probabilistic safety assessment of sea dikes in Giao Thuy-Nam Dinh

Probabilistic safety assessment of sea dikes in Giao Thuy-Nam Dinh Acknowledgments

First of all I would like to send our sincere thanks to: Assoc.Prof.Mai Van Cong and Prof Radu Sarghiuta - my supervisor from ULG and TLU - for their concern, guidance, enthusiasm, valuable advice and assistance with so much warmth and care

My high appreciation goes to all the teachers who have taught and armed me with such a valuable knowledge to my future career in my country, my colleagues, friends and my classmates for their support, assistance and for making my stay here filled with joys and memories

Pham Tien Hung

ULG-TLU-2016

REASSURANCES

SOCIALIST REPUBLIC OF VIETNAM INDEPENDENCE - FREEDOM - HAPPINESS

REASSURANCES

Dear: The management board of Thuy Loi University;

The management board of Liege University;

My name: PHAM TIEN HUNG

Major: Sustainable Hydraulic structure

Student Number: 148ULG07

I hereby declare that i am the person who conducted this master thesis under the guidance of Assoc.Prof Mai Van Cong and Prof.Radu Sarghiuta with the research topic “Probabilistic safety assessment of sea dikes in Giao Thuy-Nam Dinh”

This is a new research topic which does not overlap with any dissertation before, so there is no copy of any public dissertation The contents of the thesis are presented in accordance with regulations, the data resources and materials used in research are quoted sources

If there is any problem with the contents of this thesis, I would like to take full responsibility as prescribed

Hanoi, August 15, 2016 Applicant

PHAM TIEN HUNG

TABLE OF CONTENT

TABLE OF CONTENT

Contents

Acknowledgments 1

REASSURANCES 2

TABLE OF CONTENT 3

CHAPTER1: INTRODUCTION 1

1.1 Background and justification 1

1.2 Aim of study 1

1.3 Study approach 2

1.4 Outline of study 2

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA 3

2.1 Current status of sea dike system in Giao Thuy – Nam Dinh 3

2.2 Some features of Giao Thuy sea dikes 3

2.3 General assessment of current situation of sea dike system in Giao Thuy district 9

2.4 Some natural boundary condition in Giao Thuy - Nam Dinh 10

a) Delta topography 10

b) Soil characteristics and Geological features 10

c) Sediment transport conditions 11

d) Climate and Meteorology 11

e) Oceanography 12

f) Winds 13

g) Waves 14

CHAPTER 3: Probability risk and reliability assessment 15

3.1 General introduction 15

3.2 General background of probability theory 16

a) Risk analysis 16

b) Reliability analysis 17

3.3 Probabilistic reliability analysis of sea dikes system in Giao Thuy-Nam Dinh 23

a) Wave overtopping 25

b) Mechanisms of instability of armour layers of revetment 27

c) Toe foot instabilities 31

d) Piping 32

e) Sliding of dike slope 34

CHAPTER 4: Applying probabilistic reliability analysis to safety assessment in Giao Thuy – Nam Dinh 36

4.1 Wave overtopping 36

4.2 Instability of armour revetments: 40

TABLE OF CONTENT

4.3 Toe foot instabilities 45

4.4 Piping 48

4.5 Sliding of dike slope 53

4.6 Probability of dike system failure 55

CHAPTER 5: Conclusions and recommendation 60

5.1 Conclusions on safety of the sea dikes in Giao Thuy 60

5.2 Recommendations 61

References 63

Appendix 1: The parameters of Giao Thuy sea dike design according to technical standards in sea dike design (2012) 64

a) Grade of structure 64

b) Design water level 65

c) Deep-water wave 65

d) Design wave nears the toe of the dikes 67

e) Required free board by wave overtopping 70

f) Design revetment thickness (technical standards in sea dike design 2012) 73

Appendix 2: Geotechnical document used in calculating sliding of dike slope 74

Appendix 3: Determining failure probability of sea dike system in Giao Thuy by using OpenFTA software 76

Appendix 4: Fragility curve 84

LIST OF FIGURES

Figure 2 1: Map of sea dike system in Giao Thuy-Nam Dinh 3

Figure 2 2: Erosion in dike slope of Giao Thuy sea dike 4

Figure 2 3: The flood caused serious damage on field region in Giao Thuy-Nam Dinh 5

Figure 2 4:Damage of dike section due to Typhoon 1 (2016) 6

Figure 2 5: Dike section improved by funding of PAM 7

Figure 2 6: Sketch of double sea dike system at Giao Thuy district (ceg_mai_2004) 7

Figure 2 7: Representative cross section of sea dike in Giao Thuy-Nam Dinh (ceg_mai_2004) 8

Figure 2 8: Main seasonal wind directions in northern Vietnam 13

Figure 3 1:Frame work of risk analysis (see CUR 141, 1990) 16

Figure 3 2:Definition of a failure boundary Z=0 17

Figure 3 3:Definition of probability of failure and reliability index 22

Figure 3 4: Fault tree of Giao Thuy sea dike 25

Figure 3 5: Damage of sea dike caused by wave overtopping 26

Figure 3 6: Pore pressure in the subsoil during wave run-down (Pilarczyk et al, 1998) 28

Figure 3 7: Schematization of scour mechanism at Namdinh revetment 31

Figure 3 8: Mechanism of piping at sea dike 32

Figure 4 1: The normal distribution of MHWL based on BESTFIT software 37

Figure 4 2: Contribution of parameter to overtopping failure mode in current dike 39

Figure 4 3: Contribution of parameter to overtopping failure mode in dike according to design standard 2012 40

Figure 4 4: Contribution of parameter to instability armour of revetment in currently 43

Figure 4 5: Contribution of parameter to instability armour of revetment according to design standard 2012 44

Figure 4 6: Contribution of parameter to toe foot instabilities 48

Figure 4 7:Contribution of parameter to piping failure condition 1 51

Figure 4 8:Contribution of parameter to piping failure condition 2 52

Figure 4 9: Safety factor of slope stability calculation in Outer slope SFmin=1.501 54

Figure 4 10: Safety factor of slope stability calculation in Inner slope SFmin=1.335 54

Figure 4 11: Fault tree analysis of Giao Thuy sea dike system for present situation 56

Figure 4 12: Fault tree analysis of Giao Thuy sea dike according to Dike Design Standard (2012) 57

Figure 4 13: Fragility curve as a function of the design wave height (Hs)-Appendix 4, page 93 59

Figure A1 1: The Mean High Water Line in Giao Thuy - Nam Dinh 65

Figure A1 2: Plan of regions used to determine the parameters of deep-water wave 66

Figure A4 1: Fragility curve as a function of the design wave height (Hs) 85

LIST OF TABLES

Table 2 1: Sediment load composition on the shoreline of Giao Thuy 11

Table 4 1: Stochastic variable for mechanism of wave overtopping 38

Table 4 2: Failure probability of the dike due to overtopping 38

Table 4 3: Contribution of parameter to overtopping failure mode 39

Table 4 4: Stochastic variable for instability armour of revetment 42

Table 4 5: Failure probability and contribution of parameters to instability armour revetment in currently by using VAP 43

Table 4 6: Failure probability and contribution of parameters to instability armour revetment in dike according to dike design standard 2012 by using VAP 44

Table 4 7:Stochastic variable for mode of toe foot instabilities 47

Table 4 8: Failure probability and contribution of parameters to toe foot instabilities by using VAP 47

Table 4 9: Stochastic variable for mode of piping 50

Table 4 10: Failure probability and contribution of parameters to piping failure condition 1 by using VAP

51

Table 4 11: Failure probability and contribution of parameters to piping failure condition 2 by using VAP 52

Table 4 12: Failure probability of sliding of dike slope in Outer slope and Inner slope by using VAP 54

Table 4 13: Overall probability of failure at Giao Thuy sea dikes 56

Table A1 1: Safety standard and grade of sea dike 64

Table A1 2: The parameters of deep-water wave in region Hai Phong-Ninh Binh 67

Table A1 3: The results of wave transportation by using SWAN1D software 69

Table A1 4: Average overtopping rates are allowable according to Technical standards in sea dike design (2012) 70

Table A1 5: The required crest free board according to q=10 (l/s/m) 72

Table A1 6: The crest level of Giao Thuy sea dike according to safety design standard 72

Table A2 1: Test result of physical and mechanical properties of soil layer 1 74

Table A2 2: Test result of physical and mechanical properties of soil layer 2 74

Table A2 3: Test result of physical and mechanical properties of soil layer 3 75

Table A2 4:Test result of physical and mechanical properties of soil layer 4 75

CHAPTER1: INTRODUCTION

CHAPTER1: INTRODUCTION

1.1 Background and justification

Vietnam is a typhoon prone country located in the tropical monsoon area of the South East Asia The majority of Viet Nam population lived in the low lying river flood plains, deltas and coastal margins which involves mainly in agricultural and fishery sectors In recent years, evolution of natural disasters and weather in Viet Nam was complications, typhoons from the South China Sea bring torrential rainfall and high winds to the coast and further inland On average four to six typhoons attack the coast annually resulting in heavy damage, loss of life, and destruction of infrastructure facilities and services The reason why the water disasters are so serious is that most

of the population lives in areas susceptible to flooding Thus the formation and development of defensive system are always attached to life and production of people from generation through the generation

Nam Dinh province in general, Giao Thuy district in particular constitutes part of VietNam’s with a long line of dikes and sea defenses Most of the sea dikes are built over the centuries mostly due to local initiatives and have generally an inadequate design and are poorly constructed Due to the bad state of the dikes a significant part

of the yearly funds has to be allocated to repairs and maintenance

Although, before flood season in every year, several researches on the safety assessment of the coastal defenses system have already been conducted but these researches ’s weakness were done based only on what already happened of the sea defenses system in the previous years and the experiences on management of the monitors As a result, the risk of the damages is still going on at the high rate and frequently and establishing method for assessing safety of sea dikes based on reliability analysis theory is necessary

1.2 Aim of study

Probability safety assessment of sea dikes in Giao Thuy-Nam Dinh The aim of this

CHAPTER1: INTRODUCTION

study can be outlined as follows:

reliability analysis theory

thesis

1.3 Study approach

on reliability analysis theory at home and abroad

1.4 Outline of study

natural boundary condition

reliability analysis to safety assessment in Giao Thuy-Nam Dinh are presented

in chapter 3 and chapter 4 There will be investigated all kind of failure modes which may occur and estimated which factors have the greatest impact to the failure of sea dike

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

2.1 Current status of sea dike system in Giao Thuy – Nam Dinh

Long ago, sea dike system has played vital role in the natural disaster consequences prevention and mitigation Furthermore, in the present recessionary conditions, defense system also has essential role as protection for residential and urban areas to ensure the sustainable economic development

Giao Thuy is a coastal district of Nam Dinh province, 35 km South away from Nam Dinh city It is bounded on the Northwest by Xuan Truong district and Southwest by Hai Hau district and also borders Thai Binh on the North and Northeast

Giao Thuy district has natural area of 230.22 square kilometers and population of 256,864 people (counted in 2010), surrounded by 27 km of sea dikes from So estuary

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

were not sufficient while the actions of strong storm surges and typhoons are getting stronger The specific features can be listed as following:

2004 with a length of 2580 m at the positions such as: K15.603 ÷ K15.903; K20.350

÷ K22.267; K 23.685 ÷ K23.935 located majority in Co Vay, Thanh Nien sluice, Ang Giao Phong Due to the innovation in a lot of times, Giao Thuy sea dikes is not ensured In several places, dike sections (K22+400  K27+161) are influenced by

Giao Lam

Figure 2 2: Erosion in dike slope of Giao Thuy sea dike

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

thickness of sand in front of dike and the rate of structural erosion is from 10m to 15m per year If there are not sufficient and in-time counter methods, this problem leads to fast retreat of coastline

and beach erosion due to wave actions and storm surges, typhoons is approximately 20,000ha

Figure 2 3: The flood caused serious damage on field region in Giao

Thuy-Nam Dinh

affected by salt water infiltration and 70,000 tons of food was lost, salt mining fields, and shrimp hatching ponds were also heavily damaged, according to figures from Tuoitre Newspaper

people and huge property loss In 2012, the damage caused by the Typhoon 8 adds

up to over 655 billion VNĐ

meter of stone were taken away from the sea dikes due to Storms surge accompanied with high tides

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

Figure 2 4:Damage of dike section due to Typhoon 1 (2016)

In the recent years, the dike slope and revetments were improved by funding of domestic and international organizations (PAM) to assure the storm’s a category 9 and the average tide level of 5% However, the landslides and dike break may happen

if Giao Thuy sea dikes have affected the design frequency exceeding above design

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

Figure 2 5: Dike section improved by funding of PAM

The structure typically of Giao Thuy sea dikes system shown in Figure 2.6, included two dike layers in each section

Figure 2 6: Sketch of double sea dike system at Giao Thuy district

As a matter of fact, the determining factor of durability of the dikes is the earth core

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

consisted of material from local sand and clay resources The revetments on top of outer slope was built on natural stones or artificial blocks on a layer of clay

The typical parameters of representative cross section of this sea dike as Figure 2.7 below:

Figure 2 7: Representative cross section of sea dike in Giao Thuy-Nam Dinh

(ceg_mai_2004)

approximately 250kg

Two functions of sea dike system in Giao Thuy are flood defense and protection of inland from erosion This means that the dikes must be stable in any case However, nearly all the dikes which were constructed in the past only based on the experiences

of the local people and designed by very old method The dikes system seems to be insufficient respect to the actual boundary conditions for the time being These failures caused flooding in the wide area along Giao Thuy coastline and as the consequence, it leaded to loss of land, economic archives and even loss human’s life

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

2.3 General assessment of current situation of sea dike system in Giao Thuy district

Long ago, defense system played an important role in flood prevention works Giao Thuy is a coastal district, not only affected the flow of the river, but also influenced

by the sea So that the sea dike system has an important task in contributing to political and economic stability of Giao Thuy district in particular and Nam Dinh province in general

The sea dikes in Giao Thuy was built from long years ago (about 250 years) on soft ground raised by Red river This dike system affected directly by tide, typhoons and flood flow from rivers into South China sea Especially, dike break and landslides often happen when heavy storm combined with high tide in Giao Thuy dike

In the middle of dike system, sea gains on land caused of the loss of dike and people

in the area Moreover, the landslides and dike breach occurred frequently had an adverse effect on production activities and life of the people in Giao Thuy That results caused by the low standard of soil on dike body, lack of reasonable of material

in armour revetments and toe dike, the deterioration and damage of old sluice systems

In addition, the level design standard of sea dike is low, therefore it does not meet flood prevention and control requirement in current situation of Giao Thuy This problem will cause serious damage when there was a combination of surge and high tide

In the recent times, the damage caused by natural disasters tends to increase in Worldwide, along with the global climate change These storms tend to come up stronger, becoming super typhoon while the phenomenon, rain, winds, tornadoes also occur more frequently caused more serious consequence

The activities in economic and social life of coastal area caused the changes in the natural environment in the direction of disadvantage and increase the damage of natural disasters In many areas, mangroves and coastal forests have been lost not only cause changes in the ecological environment in ways that are harmful, which

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

also makes big waves hit straight into the sea dike, causing sea dike break

It is clear that the damages of defensive system lead to many impacts on the social and economic development in the area In fact, some sections of new sea dikes had been built by some efforts of the central and local authorities in order to keep under control the possible adverse consequences However, these efforts still keep limited

to lack of suitable design methodology as well as strategic and long-term solutions and constrained budget

So a suggestion, in this thesis, the reliability analysis theory combined the analysis of the factors affecting on flood defense system will be implemented according to research and development of methodology design A case study of research in Giao Thuy-Nam Dinh is chosen for demonstration of the method and calculating

2.4 Some natural boundary condition in Giao Thuy - Nam Dinh

a) Delta topography

Delta topography of Giao Thuy District has flat topography with an altitude vary from 10-15m to mean sea level (MSL), gradually sloping from Northwest to Southeast In the middle of the delta, mountains and hills can be found, linked to the geological formation under the alluvial sequences

b) Soil characteristics and Geological features

Soil in Giao Thuy district has alluvial characteristics because this area has been formed by the rivers in Red River system The action of waves and tide current causes the coastline shaving and the erosion is taking away the small grains causing the coarsening of the grain size of the beach

According to the geology investigation document of the Hydraulics Engineering Survey and Design Service of Namdinh, strata structure of Giao Thuy coast has 5 following layers:

plastic to stiff with thickness of 1.5 to 2.0 m

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

We can easily realize that Giao Thuy has a vulnerable beach from above structure of strata Therefore, the stability of the dike will be seriously threatened if the upper layer is washed away

c) Sediment transport conditions

From sediment investigations in Giao Thuy, it is clear that sections of the beach situated relatively far from the river mouth in the range of 10 km are not nourished

by river sediment caused by The sediment supplied by rivers is accumulated in the near shore zone close to the river mouth and is not transported along the shore in any significant amounts

Table 2 1: Sediment load composition on the shoreline of Giao Thuy

A preliminary assessment of longshore sediment transport in the coastal area of the Red River estuary indicated that the total annual longshore sediment transport is about 5% of the whole annual Red River sediment discharge that remains in the near shore zone

d) Climate and Meteorology

Giao Thuy is situated in tropical climate area with a pronounced maritime influence The winter is cool and dry, with mean monthly temperatures varying from 16oC to

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

21ºC Fine drizzle is frequent in early spring, after which the temperatures rise rapidly

to a maximum of 40ºC in May The summer is warm and humid, with average temperatures varying from 27ºC to 29ºC The prevailing winds are Northeast in the winter, and South and Southeast in the summer

The average annual rainfall is 1600 to 1800 mm, 85% of which occurs during the rainy season (April to October) The heaviest rainfall occurs in August and September, causing intensive flooding in the delta due to overflow of the riverbanks Typhoons and tropical storms are frequent between July and October During the period from 1911 to 1965 the region withstood 40 typhoons However, the frequency

of storms and typhoons appears to have increased in recent years Typhoon storms usually come from the west pacific, through the Philippines or Eastern Sea They then shoot into the coastal areas of South China and Vietnam Among the typhoons that occurred from 1954 to 1990, strong winds with grade 12 were observed for 31 cases The annual average number of typhoons is about 5, but more than 10 were observed

e) Oceanography

The sea at Giao Thuy is open sea (there is no offshore island) so the wind fetch is long enough for wave growth and approaches the shoreline without any obstacles, which can cause considerable damage to shoreline and sea dikes According to previous observation, waves at Giao Thuy had following characteristics:

- In winter (from September to March): In the winter, the sea was much more rough sea than in the summer Wave height is about 0.8m – 1.0m, with periods varying from 7 to 10 seconds Predominant wave direction was northeast, and

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

makes angles of about 30º to 45º with the shoreline

days but strong storms usually happen in this season causing severe damage to the dike system Average wave height varies from 0.65m to 1.0m with period ranging from 5 to 7 seconds The prevailing wave direction is south and southeast

f) Winds

Since there is no offshore island, and it has relatively flat and low-lying topography, Giao Thuy is an area exposed directly to the open sea, the area is subject to the winds generated from every direction In the winter time (from October to March) the dominant wind directions are north, northeast and east In summer (from May to August) the dominant wind directions are south, southeast and southwest April and September are considered to be transition times

Figure 2 8: Main seasonal wind directions in northern Vietnam

CHAPTER 2: GENERAL OVERVIEW OF STUDY AREA

g) Waves

The sea at Giao Thuy is open sea (there is no offshore island) so the wind fetch is long enough for wave growth and approaches the shoreline without any obstacles, which can cause considerable damage to shoreline and sea dikes According to observation, the waves at Giao Thuy has following characteristics:

- In winter (from September to March): In the winter, the sea was much more rough sea than in the summer Wave height is about 0.8m – 1.0m, with periods varying from 7 to10 seconds Predominant wave direction was northeast, and makes angles of about 30o to 45o with the shoreline

days but strong storms usually happen in this season causing severe damage to the dike system Average wave height varies from 0.65m to 1.0m with period ranging from 5 to 7 seconds, the prevailing wave direction is south and southeast

CHAPTER 3: Probability risk and reliability assessment

3.1 General introduction

Over the past few decades, flood defense system design has recorded breakthroughs

in its development In traditional method, dike crest level is based on maximum flood water level recorded in history This water level is determined based on statistic data called design water level defined based on design frequency

The design frequency of design water level is widely applied as a safety standard for protected area according to probability of flooding However, this theory is true in case of the break dike caused by the flood level exceeded design water level and not true in case of flood level smaller than design water level

The safety standard depended on traditional deterministic approach is design frequency of load and safety factor based on possible failure mechanisms In the way

of reliability analysis theory, the safety standard is limit states of failure probability

of system regarded as combination of failure probability of components in the system which connected closely to exceed frequency limit of load The probability of flooding is determined if the damage causes can be listed and failure probability of each component can be determined From the above arguments, idea of dike safety assessment based on failure probability analysis of all the relevant factors is feasible Principle of probability of a structure system must base on by each component those failures creative by mechanisms and model failure Calculating the probability of each component is very important when anticipated probability analysis of one structure

There are three factors when assessed probability They are Thread – mechanism – failure probability Firstly, we must list threads and mechanism A failure mechanism

is defined as a form in which structure must effected by thread

Advanced of probability analysis method is the probabilistic approach results in a

section or structure) So the probabilistic approach is an integral design method for the whole system

3.2 General background of probability theory

a) Risk analysis

In every floodplain, the accepted probability of flooding is not the same It depends

on the expected loss in case of failure, the nature of the protected area and the safety standards of the country However, risk is the product of the probability and a power

of consequence, therefore this reason accepted risk is a better measure than an accepted failure probability: Risk = (probability) * (consequence)n The power n is depended on the situation of the system, n=1 is a natural risk approach and implies the calculation of expected value while n>1 denotes the risk aversion

Figure 3 1:Frame work of risk analysis (see CUR 141, 1990)

The elements of risk analysis in the probabilistic approach are shown in Figure 3.1

At first, before making an inventory of all the failure modes and the possible hazards, the flood defense system has to be described as a configuration of elements such as dike sections, sluices and other structures Due to the miss of a failure mode can

Objective of risk analysis

Frame of Description of

the system

Possible hazard and failure modes of failures

Probability part

of the risk Quantifying

consequence

of failure

Probability of consequences Risk Evaluation Criteria Adjustment Decision

Risk acceptance

seriously influence the design safety, this step plays an important role in the analysis

In the next step, the quantifying of the impacts of failure for all possible ways of failure is carried out The probability of the failure and consequences form are a part

of the risk The design can be evaluated when the risk is calculated with the criteria available such as a maximum acceptable probability of a number of casualties A frame of reference is necessary for determining the acceptable risk The national safety level aggregating all the activities in the country can also get to be this frame

of reference The evaluation of the risk will decide whether the work can decide to adjust the design or to accept it with the remaining risk

b) Reliability analysis

The reliability function is key elements of the probabilistic calculation of ascertaining the probability of failure The function of reliability Z is formed concerning the limit state considered, in such a way that positive value of Z corresponds to non-failure and negative values to failure (see Figure 3.2) The probability of failure thus be represented as P{Z<0} The reliability function is a function of a number of stochastic variables

X 2

X 1

Figure 3 2:Definition of a failure boundary Z=0

These methods define failure probability about predetermined reliability function distributed some levels as following:

failure

Level 1:

Nowadays, the design works are based on design standards and guidelines In that way, the parameters of durability are adjusted by the coefficient characteristics and that of load are adjusted by load coefficients Shown by the following formula:

S R

R S



  (3.1)

Where:

R: Durability

S: Load

ɣR: Safety coefficient of durability

ɣS: Safety coefficient of load

The characteristic value of durability and load coefficient are calculated by formula (3.2):

k V S

progressions need to do

The general form of reliability function Z=R-S is considered In which R and S are functions of strength and load respectively and both considered following normal distribution This implies that the statistical parameter of reliability function Z can be obtained through:

( ) 2 2

1 ( )

  : Standard normal distribution for the variable β

In general Z in equation (3.10) will be a function of more than two variables These variables do not have to be normally distributed and Z does not have to be linear Only if Z is a linear function and all variables are normally distributed (and independent) the second equation in (3.10) is indeed equality and not an approximation

Z may be a function of n stochastic variables X1, X2,….,X , as both the "load", S, and the "strength", R, may depend on more than one variable In order to perform a

level II calculation, the variables X1, X2, ,X have to be independent and it must be possible to linearize the reliability function Z in all point of Z Suppose the reliability function, Z, fulfils the requirement and the variables X are all normally distributed and independent

It is supposed that the reliability function can be linearized, so tangent plane in a point

on its surface can be expressed by a first order Taylor expansion:

  = partial derivative of Z with respect to Xi, evaluate in Xi =X

The mean value and standard deviation of Z Lin are:

Z Z









Figure 3 3:Definition of probability of failure and reliability index

If mean values X1* (Xi), ,X*n (Xn) are situated, so called mean value approximation of the probability of failure is obtained If the failure boundary

is nonlinear, a better approximation can be achieved by linearization of the reliability function in the Design Point The Design Point is only defined if the variables are normally distributed (or are transformed to normal distributed variables) The Design Point is defined as the point on the failure boundary in which the Joint (normal) probability density is maxima

The design point is given:

The probabilistic approach used in this study is at level II which considers that most

of all the stochastic variables of reliability function are followed the normal distribution

3.3 Probabilistic reliability analysis of sea dikes system in Giao Thuy-Nam Dinh

The flood defense system consists of many components made up a closed system to

protect residential areas Safety factors depend on safety standard when designed and constructed The different level of safety standard is provided in national standard and applied in design work

Thuy-The safety of defense system in Giao Thuy- Nam Dinh is assessed by determining the failure probability of each component, whole system and probability of flooding First of all, we need mapping system, identifying failure mechanisms The main failure mechanisms of sea dikes in Giao Thuy are listed below:

- Overtopping

Figure 3 4: Fault tree of Giao Thuy sea dike a) Wave overtopping

insufficient

crest of the dike

be occurred:

material of filter layer is washed

Overtopping Piping Sliding of dike

slope

Toe foot instabilities

Instability of armour

layer

- Damage of upper part of revetment due to the return flow of overtopped sea water

Figure 3 5: Damage of sea dike caused by wave overtopping

It is clear that, the crest level of the dikes and the strength of crest wall are the most important parameters to avoid these failures due to wave overtopping

The design water level is the first component which mainly contributes to crest height

of a dike This water level corresponding to design frequency and design life time of structures should be the highest water level which may occur at the location Normally the design water level includes mean water level, tidal level, storm surges, wind setup, wave setup

Wave run-up level is the second important component contributed by wave height at the location near the toe of the dikes It is so called local design wave height for the dikes Wave run-up depend on the outer slope, which can consist of materials by different roughness If there is a berm, the berm width is also a parameter which can influence the magnitude of the run-up and overtopping of incident waves, and the impact on slope protection

The reliability function of overtopping:

Z : Maximum water level acts on the dike (including wave run-up level)

The failure presents when Z<0, therefore the probability of overtopping failure mode

is P(Z<0)

b) Mechanisms of instability of armour layers of revetment

In VietNam, one of the most regular failure is instabilities of the armour layer of the revetments There are some main reasons which caused the failure At first, the thickness of the cover layer is not sufficient to the hydraulic condition due to the fact that most of the dike designs were applied old method of the year 60s Secondly, the quality of the constructions was not good because the revetments implemented mostly

According to Dikes and revetments, Krystian W.Pilarczyk editor, when the water moves on a revetment structure it can affect the subsoil, especially, when this consists

of sand This effect is considered within the framework of the soil- mechanical aspects and can be of importance to the stability of the structure, see Figure 3.6 There are three aspects that will be discussed within the framework of soil- mechanical aspects: elastic storage; softening (liquefaction); and drop in the water level The background information can be found CUR169/RWS (2001)

Figure 3 6: Pore pressure in the subsoil during wave run-down (Pilarczyk et

al, 1998)

the grain skeleton and the compressibility of the pore water (the mixture of water and air in the pores of the grain skeleton) Because of these characteristics, wave pressures on the top layer are passed on delayed and damped to the subsoil

of the revetment construction and to deeper layers (as seen perpendicular to the slope) of the subsoil This phenomenon takes place over a larger distance or depth as the grain skeleton and the pore water are stiffer Elastic storage can lead to the following damage mechanisms (Stoutjesdijk, 1996):

For the stability of the top layer, elastic storage is particularly of importance if the top layer is placed directly on the subsoil without granular filter

Because the revetment construction consists of a top layer on a filter layer, the thickness of the filter layer may in these diagrams be partially or completely (depending on the type of revetment) added to the thickness of the top layer The

equivalent thickness is defined as:

Deq : is the equivalent thickness of the top layer

D : is the real thickness of the top layer

b : is the thickness of the filter layer

∆t : is the relative mass (weight) under water of the top layer

with liquefaction, water overtension is connected with a plastic deformation of a grain skeleton instead of an elastic deformation Water overtension through softening occurs when the grain skeleton deforms plastically to a denser packing With regard to liquefaction, according to Dutch criteria, with a top layer on a granular filter there is generally no danger of liquefaction

or a ship passing through a waterway or canal As with placed stone revetments, the resulting uplift is especially dangerous when the top layer is sanded up due to which the permeability of the top layer may decrease in time

is (representative) relative density of the top layer (-),

D is (representative) thickness of the top layer (m)

top

k Db k

 

In which:

bf is thickness of the filter layer (m);

kf is permeability of the filter; ktop is permeability of the top layer;

D is thickness of the top layer

The common form of reliability function of armour layer of revetment is:

: is relative density of applied material

D: is the size of elements

c) Toe foot instabilities

The maximum scour depth in front of the toe structure is used to determine the protective required depth for the toe structure obviously During the life time of structures, the maximum depth of scour is regarded to an equilibrium scour depth From practical experience, that depth should lie from 0.5 to 1.0 times significant wave height (Pilarczyk et al, 1998) Basing on both model of mathematics and physics, there are several researches on scour development near and around the toe of marine structures

However, the scour mechanisms and their depths depend on so many parameters and are very complicated

Figure 3 7: Schematization of scour mechanism at Namdinh revetment

Analysis the stability of the toe by the recent method in order to know about it’s working state Based on that, the suggestion for design of the toe will be given The

( ) 2 sinh

x s

The reliability function of this situation is defined as follow:

of dike foundation move continuously to downstream Processing happen for a long time will lead to appear a sand low on dike foundation, it makes empty dike foundation and threads the reliability of dike body

Figure 3 8: Mechanism of piping at sea dike

The failure mechanism of piping occurred when two conditions must be satisfied:

The first condition: foundation clay layer is rupture when pressure of seepage flow

exceeded saturated volume weight So the reliability function of the first condition is:

Z  gd g H (3.22)

In which:

is saturated volume weight of foundation layer

is volume weight of water

d is clay layer depth from toe of the dike to layer of sand

g is acceleration of gravity

The second condition: Based on the Bligh's criterion in the reliability function of

c = c B constant depending on soil type, according to Bligh

investigated

e) Sliding of dike slope

A fixed set of conditions and material parameters are considered to be a base for computing the factor of safety in the deterministic slope stability analyses The slope

is considered to be unstable or susceptible to failure, if the safety factor is greater than the unity